A number of extensions and variations seem possible. [1]} consider multi-modular models which are in conflict because shared parameters have different priors in different models. They use Markov melding to bring these together in a single model with pooled priors. The pooled priors represent a kind of consensus across modules. This could be combined with SMI if some individual generative models are mispecified.
In dictatorial pooling the pooled prior is taken to be the prior in one “authoritative" module.
This may lead to misspecification in modules sharing the parameter. This is a setting suitable for SMI, where we know which modules are misspecified and need to modulate their influence on inference in the authoritative module.
